There is evidence (discussed in §REF ) that a chiral spin-liquid phase arises in a small but finite range of \(U/t\)  in the undoped Hubbard model on the triangular lattice. Moreover, for a band-structure with a symmetry protected quadratic band-touching, there is a dominant tendency toward an anomalous quantum Hall state at weak coupling [1]}. Although these states break time reversal symmetry, they must have a zero orbital current on any link lying in a mirror plane. However, a CDW state in doped versions of either of these seems likely to support orbital loop current order.
